6 problems

E2-degeneration conjecture. This Leray spectral sequence degenerates at $E_2$.

Let $M$ be the motive associated with the cohomology under consideration, and let its motivic cohomology map by a regulator to Deligne cohomology. The motivic classes determine a m…

Beilinson's conjecture. With notation as above, if a class in $CH^n(X)_{\mathbb Q}$ vanishes in $H^i\left(k,H^{2n-i}(X_{\bar k},\mathbb Q_\ell(n))\right)$ for $i=0,1$, then it does…

Let $Y$ be a smooth projective variety over $\overline{\mathbb Q}$. Write $CH^*(Y)_{\mathbb Q}$ for the Chow ring with rational coefficients, and let rational Deligne cohomology be…

Kato's distinguished-triangle conjecture. There exists a natural distinguished triangle

Let $X$ be a complex manifold, and let $E$ and $F$ be holomorphic vector bundles over $X$ that are $C^{\infty}$-isomorphic. Nadel's relative invariants are denoted by…